Lemuel Falk, a ``randomnist'' from the Steklov Institute in Russia
gets a visiting position at a chaos research institute in Upstate New
York in this academic farce. He meets a drunkard who studies the
chaotic aspects of water droplets (especially tears), a Harvard MBA
who runs the local supermarket, a sexy barber/drug dealer named
``Occasional Rain Morgan'', and a dope smoking rabbi from Brooklyn who
believes ``God is Randomness.''

Yo! The thing is, halfway through reading this book, I sort of fell
in love with it, which isn't at all what I expected to do from the
start. At the start, the characters were flat parodies of researchers
at a mathematics institute and the ``ordinary people'' that populate
the town. The jokes were funny enough, but I didn't expect it to go
anywhere. Moreover, the author's obvious ignorance of some key
results in the areas of mathematics that are frequently discussed in
the book were a source of disappointment. So, I even went as far as
to write a review of the book which I posted here (prematurely)
treating it as a funny but lightweight book that gets the math all
wrong.

But, something unexpected happened. The characters get fleshed out,
some serious subtexts are addressed (even as the characters discuss
and denounce the whole notion of subtexts in novels) and an
interesting if somewhat flawed characterization of mathematicians and
mathematics gets deeper than I initially expected.

This book is all over the place. In addition to being a broad farce, it is

a somewhat touching (though, I must warn, also quite kinky) love story
between the middle aged Russian researcher and the young barber

a murder mystery in which Falk determines the identity of serial
killer using game theory and his expertise in randomness

a philosophical exploration of the deep questions of life (in
this case: is the universe random or just chaotic? do we have free
will? what is ``god''?)

a psychological drama in which a man overcomes the scars
inflicted on his psyche in his youth by his role in the death of his
father

and, of course, mathematical fiction!

Mathematically, there really are some interesting things to say
about the relationship between chaos and randomness, and the author
seems to have understood just a few of those things and based the book
around them. In particular, it is true that the mathematical field of
chaos theory has provided us with numerous examples of very simple
deterministic rules whose resulting output looks random to a
naive observer and which is unpredictable (in the very practical sense
that even though the system is completely deterministic, you need to
be able to measure the present state of the system much more precisely
than we can in the real world to be able to make accurate predictions
about what will happen next). The corollary is that when we look at
things that we really think of as random (like a coin flip) we now have reason to wonder whether they are really random or whether they are
simply chaotic systems.

Unfortunately, in discussing this, Littell makes a few errors that
reveal his ignorance of some of the basic theorems of chaos theory.
For instance, at one point, he uses the motion of planets in our solar
system as an example of a system which is not chaotic. I can
see why one might think so. After all, the planets seem to be quite
orderly and predictable. Ironically, however, it is precisely this
system (the motion of more than two massive objects in three-dimensional space
under the influence of gravity) in which chaos was first identified.
[The word chaos was not used, but the hallmark of chaos which we call
``sensisitive dependence'' was noticed by the mathematician Poincare
when he realized that his prize winning paper which purported to be
able to predict the motion of the planets from Newtonian principles
was flawed!] On the same page, he has Falk define chaos as ``order
without periodicity''. My objection here will be quite technical, but
the fact is that this definition is way off. For instance, the
quasi-periodic solutions to integrable systems are good examples of
order without periodicity, but they are certainly not chaotic
systems. Moreover, one of the most famous results in chaos theory is
that ``period 3 implies chaos''. Under the Li-Yorke definition of
chaos, in fact, chaos necessarily contains periodicity. [To tie this
together, the orbit of the planets is a (near) periodic submanifold
in the chaotic system which is the many-body problem.]

The author's naivete also is revealed through things he fails
to mention. It is odd to me that he talks about ``randomness'' and
``randomnists'' without mentioning probability. (Probability is the
area of mathematics that really studies randomness and the
practitioners are called probabilists.) He also seems unaware of the
results of mathematical physics. Any late 20th century scientist
interested in the question of whether randomness is real would have to
bring up the topic of quantum theory. After all, it is the
apparent unpredictability of the collapse of the quantum wave function
which is the most obvious candidate for true randomness in the
real world. However, this topic is never even discussed. Nor does
Falk seem to know General Relativity, since his description of the
number pi refers to the diameter and circumference of the
circular path of a space ship travelling around the universe...which
probably would not be pi because of the curvature of spacetime.

Unfortunately, Littell is also not very good at imagining impressive
mathematical results. Supposedly, Falk has become famous for looking
at finitely many digits in the decimal expansion of pi and failing to
find any order. This is hardly the sort of result that would generate
as much attention as his result supposedly did. Also, his idea for
using pi in cryptography seems a bit lame. Finally, the ``message''
that Falk and Rain find hidden in pi is ridiculously weak compared to
the one in Sagan's Contact.

One final complaint: although Littell seems to have done his homework
on the Jewish angle of the story, a few strange aspects may grate on
the nerves of a Jewish reader. For instance, the rabbi uses ``goys''
for the plural of ``goy'' (I'm sure he would have said ``goyim'') and
also uses ``goy'' as an adjective (when ``goyishe'' is the adjectival
form).

But, as I said, there are lots of things I love about this book. I
love the way Falk collects American colloquialisms. I love the
anecdote about the chaos professor in Leningrad who -- because of
problems with the Party -- lectures on subway trains for students who
stuff rubles in his pockets. I think the author does capture some
aspects of what it is like to be in a mathematics ``think tank''.
And, of course, he does a great job of parodying the current state of
American culture. Perhaps my favorite scene was when he visits a math class
at Backwater University as a guest lecturer and speaks to the students about
randomness and pi in the slang dialect he has picked up from Rain.

Highly recommended!

Contributed by
Anonymous

Despite the flaws in maths, his brilliant writing ability, plus the overarching
grandeur of the story he tells, makes this one of my favourites novels.

Contributed by
John C. Konrath

There are parts of this novel that I enjoyed very much and other parts which I detested. Mr. Littell's remarks concerning the American college system were skillfully delivered. However, I found the explicit sexual content pornographic and out of step with the general theme of the work. There are numerous quotable lines for those who are interested in such things.

Note: Littell is better known as an author of straight-up spy stories, such as The Once and Future Spy, which features a character, Huxstep, who impresses strangers with his lightning fast mental arithmetic. This trait alone does not seem sufficient to give this book its own entry in the database, but it probably is worth mentioning here, and I would like to thank Michael Henle for bringing it to my attention.